The object of this section is to give narratives illustrating the
treatment of concurrent events in two cases. The first is when
two sub-narratives do not interact, and the second is when they
do. The first sub-narrative is ordinary block stacking (as
discussed in many situation calculus papers), and we suppose the
stacking to be done by a person called Daddy in New York. In the
second sub-narrative, the actor is named Junior, and he wants to
fly from Glasgow to Moscow via London. The story is taken from an
earlier unpublished but widely circulated manuscript [McCarthy, 1992]
discussing how circumscription could be used to treat an
unexpected obstacle to a plan. In this case, Junior may or may
not lose his ticket in London. The change is made by adding a
single sentence to the facts. Without that sentence, one can
conclude that flying to London and then to Moscow will get Junior
to Moscow. With it he must buy another ticket in London, i.e. we
can no longer conclude that the original sequence of actions will
work, but we can conclude that the revised sequence that includes
buying a ticket in London will work.

Because we want to treat interacting events, we make life more
complicated for Junior. If he loses his ticket, he must wire
Daddy in New York for money. Daddy, who normally indulges Junior,
has to interrupt his block stacking and sell a block in order to
get the money to send Junior.

Narrative 1

In this narrative Junior doesn't lose his ticket and gets to
Moscow without asking for help. Daddy stacks blocks in New York.
There is no interaction, and nothing is said about the time
relations between the two sub-narratives.

When Junior is in London, inertia gets us that the flights
still exist, and Junior still has Ticket2. As for Ticket1, we
would infer that he still has it unless we brought in the fact
that a ticket is used up when one takes the flight the ticket is
for. That is certainly a part of the knowledge of anyone who
travels using tickets. Thus someone who had travelled by bus
would infer it about airplane travel. Indeed it could be inferred
from more general principles about commerce, e.g. that a seller
doesn't want to allow the buyer to get an arbitrary number of what
he has a paid for one of. However, anyone who travels has the
more specific information and doesn't need to infer it from general
principles about commerce. Indeed he may never have formulated
any general principles about commerce.

Now we begin Daddy's life as a block stacker. We have stated no
relation between the situations S0 and S0' and know nothing
of their temporal relations. If we asserted

then we could conclude that Junior still had the tickets in
S0'. Also asserting S0' = S0 would do no harm to the
conclusions drawn about either subnarrative. We have asserted
that Daddy has the three blocks mentioned, and we would like to
be able to draw the nonmonotonic conclusion that these are all
the blocks he has.

We can imagine that blocks being clear is a precondition for
moving them. The preceding subnarrative does not violate this
precondition, but in a narrative we don't ordinarily have to show
that preconditions are satisfied. We should be able to conclude
via inertia that Daddy has the three blocks in the final
situation.

Narrative 2

Now Junior loses the ticket and sends a telegram to Daddy
asking for money. Daddy, who normally indulges Junior, sells
a block and sends Junior the money, who buys a London-Moscow
ticket and goes on to Moscow. I chose a telegram rather than
a telephone call, because I would not want to tell about a
telephone call as a sequence of statements by Junior and
Daddy but rather to regard its result as a joint action,
e.g. an agreement that Junior and Daddy would do certain
actions.

Note also we haven't treated what Daddy now knows as the
result of the telegram. It seems that treating knowledge and
treating agreement are similar in their requirement for
treating intentional entities. The intentional state that
Junior has requested that Daddy send him the money is not
merely that Daddy knows that Junior wants Daddy to send him
the money. Also the agreement is likely to have something
like a bit of narrative as an argument, e.g. a set of
actions that Junior and Daddy will do with only partial time
relations between the actions.

Up to here, narrative 2 is the same as narrative 1. Also insert
here the sentences between equations (16) and
(31).

We want to regard losing the ticket as something that happens
to Junior rather than as something he does. That's why we don't
write . The bad consequences of doing
the latter would arise when we get around to writing laws that
quantify over voluntary actions.

We will use some of the same names now for situations that are
different than in narrative 1.

Interpolating unconnected situations and events into a narrative
should not harm the conclusions. For example, we could put
situations S0.5 and S0.7 between S0 and S1, i.e.
time(S0) < time(S0.5) < time (S0.7) < time(S1),
and suppose
that Junior reads a book on the airplane during the inner
interval. The previous statements
about what holds when Junior arrives in London should still seem
ok. However, suppose we postulate that Junior spent time in
Peking on the way from Glasgow to London. This would make the
narrative anomalous, but some geograhical knowledge is
required to make the anomaly apparent.